How to UV unwrap with repeating texture?
You can use two different UV Maps for the floor: the first for the wood texture and the second for baking shadows and lights.



Moreover, since the wood texture is seamless, you can scale the islands of the wood UV Map in the UV editor to get the size you prefer (i.e. the islands can be bigger than the 0-1 UV space). Contrariwise, all the islands of the shadows UV Map must be placed in the 0-1 UV space. Make sure you have selected the correct UV Map before baking (use the camera icon), and save externally the baked map.

When you deal with two (or even more) UV Maps, your shader is a bit more complicated. Just create a group of nodes to control the repetition of the main wood texture, and another to control the baked map. To do this, use the Input > UV Map node in the shader editor, and type the right UV Map's name.

This image shows a simple idea to create a shader which manage the two UV Maps:



Of course, your shader can be more complex, but the idea here is how to separate the nodes that control the shadows and the nodes that control the wood texture. 

P.S.: I suggest to save the baked map in PNG format with transparency, so you can use it as a mask to blend the two main node groups.